Question

In a right prism, the base is an equilateral triangle. Its volume is $80\sqrt{3}$ $c{m}^3$ and its lateral surface area is $240$ $c{m}^2$. Find its height.

Answer 1

Let the side of the base be a cm. Let the height of the prism be h cm/

$\left(\frac{\sqrt{3}}{4}{a}^2\right)h=80\sqrt{3}$ .....(1)

$\left(3a\right)\left(h\right)=240$ .....(2)

Dividing 1 by 2,

$\frac{\sqrt{3}}{12}a=\frac{\sqrt{3}}{3}$

$a=4$

Therefore, $h=20$ $cm$